Numerical approximation of RBSDEs via regularization

We design a numerical scheme based on a regularization approach to approximate the solution of reflected backward stochastic differential equations (RBSDEs). This scheme provides an approximation of the solution from above, as a difference from other existing numerical schemes. We study the order of convergence between the continuous regularized solution and the reflected solution, in full generality, as a function of the regularization parameter: the convergence order is 1/2 in Lp (p ≥ 2) for every solution component, improving to 1 in the almost-sure sense for the value process. Additionally, we derive the convergence rate of the discretized version of the regularized RBSDE to the true version under mild regularity conditions and we obtain the convergence order 3/8 in L2 sense. To illustrate these results, we perform several numerical experiments for one-dimensional American put options.